I've tried to research your question in the past because my daughter is also flat footed. I feel she lacks a "spring" in her step. Some girls just seem to bounce off quite easily and high. I never found an answer to this question or how flat feet affects tumbling, punching etc. I think perhaps it does affect it a bit but there are several elite gymnasts who have flat feet and it has not affected them. So perhaps good training and technique is vital. My daughter is a second year level 10 right now. I feel her flat feet somewhat requires more effort on her part to tumble or punch, but she is able to do all the skills thrown her way. I feel the biggest concern of flat feet is injuries. Flat feet can affect the proper alignment of the body and can cause knee pain/injuries, hips and back. I also noticed my daughter's feet seems more flat than it was.